( 849 ) 
Let us divide numerator and denominator of the last fraction by 
xl, we then find an equation of the form 
Now 
ap) 
apy lk (5) 
de (2) 
wie 
TL 
SO 
a(") 
v& 
8 
d| — 
Lv 
By the substitution 
the equation (1) passes into the linear equation 
do F,(u) + vF (wu) er 
du E(u) gaat 
3. Out of (2) we find at the same time, when the original equation 
is separated by the substitution: 
a. If F,(uw) = 0, we have H, =O, therefore 
dy Hed (y,2) 
dae He (ya) 
i.e. a homogeneous equation. 
b. If F,(u)=0, so H,=0, we have 
dy A" —"i(y,a) 
RE Et Doa 
and 
do | Fu) 
du ' Fw) 
c. If #,(u) =0, we have simply 
